This research proposes a new framework for constructing preference functions when the consequences of a decision are judged by multiple attributes or criteria. Methods for assessing single-attribute preference functions have been well established. In this work, no symmetry assumption is necessary, as each multiattribute preference function is tailor-fit to only those regularities that exist in a particular problem setting. Those parts of the preference function that are subject to simplifying assumptions are decomposed using a new classification scheme to derive further independence assumptions for the standard models. Those parts of the preference function that are indecomposable are handled using a new discretization scheme along with a behaviorally motivated interpolation rule to fill the gaps. The flexibility of these methods allows an analyst to make trade-offs between the degree of accuracy desired and amount of effort needed.